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arXiv · 0904.2792

The largest and the smallest fixed points of permutations

Emeric Deutsch·Sergi Elizalde
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Abstract

We give a new interpretation of the derangement numbers d_n as the sum of the values of the largest fixed points of all non-derangements of length n-1. We also show that the analogous sum for the smallest fixed points equals the number of permutations of length n with at least two fixed points. We provide analytic and bijective proofs of both results, as well as a new recurrence for the derangement numbers.

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Emeric Deutsch, Sergi Elizalde. 2009-04-17. The largest and the smallest fixed points of permutations. https://arxiv.org/abs/0904.2792

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